Quantization

Priyanjali Yadav, R. Ramanathan

Quantized bits per sample contributes to the total length of the key generated from samples. Each quantized bit provides security against brute force attack. Ideally, the quantized bits per sample depend on either threshold levels or data range. In this paper, we are proposing a quantization method, which assigns multiple bits to samples using a single threshold and quantized bits per sample are independent of both threshold levels and data range. This quantization technique will be helpful to methods that have low quantized bits per sample. Quantization process is critical in multiple areas of communication. Quantization process highly impacts the number and agreement of quantized bits generated at transmitter and receiver. An efficient quantization method will reduce the effort of consecutive blocks for error correction and a sufficient number of quantized bits will satisfy criteria of minimum quantized bits and limitation of any domain. A well-designed quantization technique will offer more quantized bits per sample and less bit disagreement between transmitter and receiver. Quantization technique will have a high impact on future technology, which uses channel reciprocity and randomness for a dynamic key.

Ray LaPierre

Gustavo V. López, Omar J. P. Bravo

The quantization of the forced harmonic oscillator is studied with the quantum variable ($x,\hat v$), with the commutation relation $[x,\hat v]=i\hbar/m$, and using a Shrödinger's like equation on these variable, and associating a linear operator to a constant of motion $K(x,v,t)$ of the classical system, The comparison with the quantization in the space ($x,p$) is done with the usual Schrödinger's equation for the Hamiltonian $H(x,p,t)$, and with the commutation relation $[x,\hat p]=i\hbar$. It is found that for the non resonant case, both forms of quantization brings about the same result. However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the ($x,\hat v$) quantization has less oscillations than the ($x,\hat p$) quantization, the average energy of the system is higher in ($x,\hat p$) quantization than on the $(x,\hat v$) quantization, and the Boltzmann-Shannon entropy on the ($x,\hat p$) quantization is higher than on the ($x,\hat v$) quantization.

Christian Maes

Gustavo V. López, Omar J. P. Bravo

The quantization of the forced harmonic oscillator is studied with the quantum variable (x, v∧), with the commutation relation , and using a Schrödinger’s like equation on these variable, and associating a linear operator to a constant of motion K (x, v, t) of the classical system, The comparison with the quantization in the space (x, p) is done with the usual Schrödinger’s equation for the Hamiltonian H(x, p, t), and with the commutation relation . It is found that for the non-resonant case, both forms of quantization bring about the same result. However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the (x, v∧) quantization has fewer oscillations than the (x, p∧) quantization, the average energy of the system is higher in (x, p∧) quantization than on the (x, v∧) quantization, and the Boltzmann-Shannon entropy on the (x, p∧) quantization is higher than on the (x, v∧) quantization.